# [Proj] Geocentric vs. Geodetic latitude

Gerald Evenden gerald.evenden at verizon.net
Wed Apr 28 10:26:45 EDT 2004

```I believe the code for conversion is in proj.  There is a little used
option
for geocentric lat/lon as I recall.  Obviously, geocentric only applies
to
the latitude coordinate.

Normal latitude is the angle of the surface tangent to the ellipsoid
and thus
the normal to that plane from the tangent point does not penetrate the
earth's center except at the equator and pole.  Geocentric latitude is
from
the center to the reference point.

Curiously, I had never seen any data with geocentric latitude.

The equation is rather trivial as I recall.

On Apr 28, 2004, at 9:59 AM, Frank Warmerdam wrote:

> Folks,
>
> I was recently suprised to encounter locations identified as being
> geocentric that were give as a latitude and longitude.  I had expected
> them
> to be x/y/z values in meters.
>
> A client of mine, better versed in such things explained that there is
> in
> fact a distinction between geocentric and geodetic lat/long.  He wrote:
>
> >"The angle L' is called "geocentric latitude" and is defined as the
> > angle between the equatorial plane and the radius from the geocenter.
> >
> > The angle L is called "geodetic latitude" and is defined as the angle
> > between the equatorial plane and the normal to the surface of the
> > ellipsoid.  The word "latitude" usually means geodetic latitude.
> This
> > is the basis for most of the maps and charts we use.  The normal to
> the
> > surface is the direction that a plumb bob would hang were it not for
> > local anomalies in the earth's gravitational field."
>
> I need to implement some code to convert geocentric latitude to
> geodetic
> latitude.  I think I can do from the above description, but I am
> wondering
> if anyone can confirm the above description, provide a forumla or most
> importantly provide some sample latitudes in both systems I can check
> my
> work against.
>
> Best regards,
> --
> ---------------------------------------
> +--------------------------------------
> I set the clouds in motion - turn up   | Frank Warmerdam,
> warmerdam at pobox.com
> light and sound - activate the windows | http://pobox.com/~warmerdam
> and watch the world go round - Rush    | Geospatial Programmer for Rent
>
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_____________________________________
Jerry and the low riders: Daisy Mae and Joshua

```